e2n cnan-1(c- e)"(a – c)n'U8n-5 =|U8n-4 =b2-1(d – f)"(b – d)n'cn+1e2nU8n-3 =а" (а — с)"(с — е)п'dn+1 f2nb* (b – d)"(d – f)"'e2n+1cnU8n-2 =U8n-1 =a" (а — с)"(с — е)т"U8nbr (b – d) (d – f)cn+1e2n+1U8n+1a" (c – e)"(a – c)n+1dn+1 f2n+1b* (d – f)"(b – d)n+1*U8n+2This work aims to investigate the equilibria, local stability, global attractivityand the exact solutions of the following difference equationsBun-1Un-5Yun-3 - bun-5Un+1 = aun-1+n = 0, 1, ...,(1)Bun-1un-5Un+1 = aun-1 -n = 0,1, ...,(2)Yun-3 + dun-5where the coefficients a, B, y, and & are positive real numbers and the initial con-ditions u for all i =-5,-4, ..., 0, are arbitrary non-zero real numbers. We alsopresent the numerical solutions via some 2D graphs.2. ON THE EQUATION un+1 = aun-1 +Bun-1ün-syun-3-óun-5This section is devoted to study the qualitative behaviors of Eq. (1). Theequilibrium point of Eq. (1) is given byUn-1un-5Un+1 = Un-1+n = 0,1,...,(10)Un-3 - Un-5d" f2n-2br-1(b – d)n-1(d – f)n-1'U8n-10 =e2n-1cn-1U8n-9 =an-1(a – c)n-1(c - e)r-I'f2n-1dn-1bn-1(b – d)n-1(d – f)n-1'c"e2n-1an-1(c – e)n-1(a – c)n'd" f2n-1b2-1(d-f)n-1(b– d)nU8n-8 =U8n-7 =U8n-6U8n-2u8n-6U8n = U8n-2 +U8n-4 - U8n-6d" f2n-1u(f-P)u(P-9)u4bn-1(d-f)n-1(b-d)"(-dn+1 f2ndn+1 f2nd" f2n–1bn-1(d-f)n-'(6-d)"fan dn/)" (b-d)nd" f2nbr (b – d)" (d – f)"-Ib" (b – d)" (d – f)"dn+1 f2nb" (b – d)" (d – f)"d" f2n+1b" (b – d)" (d – f)"*Other solutions can be similarly proved. O Tap to view steps...U8n-2 U8n-6U8n= U8n-2 + U8n-4 +U8n-4U8n-6

Question

e2n cnan-1(c- e)&#34;(a – c)n'U8n-5 =|U8n-4 =b2-1(d – f)&#34;(b – d)n'cn+1e2nU8n-3 =а&#34; (а — с)&#34;(с — е)п'dn+1 f2nb* (b – d)&#34;(d – f)&#34;'e2n+1cnU8n-2 =U8n-1 =a&#34; (а — с)&#34;(с — е)т&#34;U8nbr (b – d) (d – f)cn+1e2n+1U8n+1a&#34; (c – e)&#34;(a – c)n+1>dn+1 f2n+1b* (d – f)&#34;(b – d)n+1*U8n+2This work aims to investigate the equilibria, local stability, global attractivityand the exact solutions of the following difference equationsBun-1Un-5Yun-3 - bun-5Un+1 = aun-1+n = 0, 1, ...,(1)Bun-1un-5Un+1 = aun-1 -n = 0,1, ...,(2)Yun-3 + dun-5where the coefficients a, B, y, and & are positive real numbers and the initial con-ditions u for all i =-5,-4, ..., 0, are arbitrary non-zero real numbers. We alsopresent the numerical solutions via some 2D graphs.2. ON THE EQUATION un+1 = aun-1 +Bun-1ün-syun-3-óun-5This section is devoted to study the qualitative behaviors of Eq. (1). Theequilibrium point of Eq. (1) is given byUn-1un-5Un+1 = Un-1+n = 0,1,...,(10)Un-3 - Un-5d&#34; f2n-2br-1(b – d)n-1(d – f)n-1'U8n-10 =e2n-1cn-1U8n-9 =an-1(a – c)n-1(c - e)r-I'f2n-1dn-1bn-1(b – d)n-1(d – f)n-1'c&#34;e2n-1an-1(c – e)n-1(a – c)n'd&#34; f2n-1b2-1(d-f)n-1(b– d)nU8n-8 =U8n-7 =U8n-6U8n-2u8n-6U8n = U8n-2 +U8n-4 - U8n-6d&#34; f2n-1u(f-P)u(P-9)u4bn-1(d-f)n-1(b-d)&#34;(-dn+1 f2ndn+1 f2nd&#34; f2n–1bn-1(d-f)n-'(6-d)&#34;fan dn/)&#34; (b-d)nd&#34; f2nbr (b – d)&#34; (d – f)&#34;-Ib&#34; (b – d)&#34; (d – f)&#34;dn+1 f2nb&#34; (b – d)&#34; (d – f)&#34;d&#34; f2n+1b&#34; (b – d)&#34; (d – f)&#34;*Other solutions can be similarly proved. O Tap to view steps...U8n-2 U8n-6U8n= U8n-2 + U8n-4 +U8n-4U8n-6

Accepted Answer

To solve the below equation for u8n.
u8n=u8n−2+u8n−4+u8n−2u8n−6u8n−4−u8n−6

U8n-2 U8n-6 U8n U8n-2 + U8n-4 + U8n-4-U8n-6